The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.
| Customer | Amount of Tip | Amount of Bill | Number of Diners | Customer | Amount of Tip | Amount of Bill | Number of Diners | |||||||||
| 1 | $ | 7.20 | $ | 78.03 | 4 | 16 | $ | 3.30 | $ | 23.59 | 2 | |||||
| 2 | 4.50 | 28.23 | 4 | 17 | 3.50 | 22.30 | 2 | |||||||||
| 3 | 1.00 | 10.65 | 1 | 18 | 3.25 | 32.00 | 2 | |||||||||
| 4 | 2.40 | 19.82 | 3 | 19 | 5.40 | 50.02 | 4 | |||||||||
| 5 | 5.00 | 28.62 | 3 | 20 | 2.25 | 17.60 | 3 | |||||||||
| 6 | 4.25 | 24.83 | 2 | 21 | 3.20 | 60.06 | 2 | |||||||||
| 7 | .50 | 6.25 | 1 | 22 | 3.00 | 20.27 | 2 | |||||||||
| 8 | 6.00 | 49.20 | 4 | 23 | 1.25 | 19.53 | 2 | |||||||||
| 9 | 5.00 | 43.26 | 3 | 24 | 3.25 | 27.03 | 3 | |||||||||
| 10 | 4.50 | 46.40 | 4 | 25 | 3.00 | 21.28 | 2 | |||||||||
| 11 | 5.55 | 57.98 | 5 | 26 | 6.25 | 43.38 | 4 | |||||||||
| 12 | 6.00 | 34.99 | 3 | 27 | 5.60 | 28.12 | 4 | |||||||||
| 13 | 4.00 | 33.91 | 4 | 28 | 2.50 | 26.25 | 2 | |||||||||
| 14 | 3.35 | 23.06 | 2 | 29 | 3.95 | 55.38 | 7 | |||||||||
| 15 | .75 | 4.65 | 1 | 30 | 5.10 | 62.39 | 6 | |||||||||
a-1. Develop a multiple regression equation with the amount of tips as the dependent variable and the amount of the bill and the number of diners as independent variables and complete the table. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
| Predictor | Coefficient | SE Coefficient | t | p-value |
|---|---|---|---|---|
| Constant | ||||
| Bill | ||||
| Diners |
a-2. Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
Tip= ____ + _____ Bill + ____ Diners
a-3. How much does another diner add to the amount of the tips? (Round your answer to 2 decimal places.)
Another diner on average adds ______ to the tip.
b-1. Complete the ANOVA table. (Leave no cells blank - be certain to enter "0" wherever required. Round "SS, MS" to 3 decimal places and "F" to 2 decimal places.)
| Source | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|
| Regression | |||||
| Residual Error | |||||
| Total |
b-2. What is your decision regarding the null-hypothesis?
(Reject/Do not Reject) null hypothesis. At least one coefficient is (different/not different) from 0.
c-1. Conduct an individual test on each of the variables. What is the decision rule at the 0.05 level of significance? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
It would be rejected if t is less than ____ or more than ______.
c-2. Which variable should be deleted?
(Bill only/Diner only/Neither) should be deleted.
The coefficient of determination _____
a-1.
| variables | coefficients | std. error | t (df=27) | p-value |
| Intercept | 1.078 | 0.495 | 2.176 | 0.038 |
| Amount of Bill | 0.058 | 0.017 | 3.444 | 0.002 |
| Number of Diners | 0.265 | 0.211 | 1.256 | 0.220 |
a-2. Tip= 1.078 +0.058 Bill + 0.265 Diners
a-3. Another diner on average adds 0.265 to the tip.
b-1.
| Source | SS | df | MS | F | p-value |
| Regression | 51.750 | 2 | 25.875 | 20.84 | 0.0000 |
| Residual | 33.524 | 27 | 1.242 | ||
| Total | 85.274 | 29 |
b-2. (Reject) null hypothesis. At least one coefficient is (different) from 0.
c-1. It would be rejected if t is less than -2.048 or more than 2.048.
c-2. (Diner only) should be deleted.
The coefficient of determination = 0.61
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